import math
import warnings
import numbers
from typing import List, Tuple, Optional, overload, Union, cast

import torch
from torch import Tensor
from .module import Module
from ..parameter import Parameter
from ..utils.rnn import PackedSequence
from .. import init
from ... import _VF

_rnn_impls = {
    'RNN_TANH': _VF.rnn_tanh,
    'RNN_RELU': _VF.rnn_relu,
}


def apply_permutation(tensor: Tensor, permutation: Tensor, dim: int = 1) -> Tensor:
    return tensor.index_select(dim, permutation)


class RNNBase(Module):
    __constants__ = ['mode', 'input_size', 'hidden_size', 'num_layers', 'bias',
                     'batch_first', 'dropout', 'bidirectional', 'proj_size']
    __jit_unused_properties__ = ['all_weights']

    mode: str
    input_size: int
    hidden_size: int
    num_layers: int
    bias: bool
    batch_first: bool
    dropout: float
    bidirectional: bool
    proj_size: int

    def __init__(self, mode: str, input_size: int, hidden_size: int,
                 num_layers: int = 1, bias: bool = True, batch_first: bool = False,
                 dropout: float = 0., bidirectional: bool = False, proj_size: int = 0,
                 device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(RNNBase, self).__init__()
        self.mode = mode
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.num_layers = num_layers
        self.bias = bias
        self.batch_first = batch_first
        self.dropout = float(dropout)
        self.bidirectional = bidirectional
        self.proj_size = proj_size
        num_directions = 2 if bidirectional else 1

        if not isinstance(dropout, numbers.Number) or not 0 <= dropout <= 1 or \
                isinstance(dropout, bool):
            raise ValueError("dropout should be a number in range [0, 1] "
                             "representing the probability of an element being "
                             "zeroed")
        if dropout > 0 and num_layers == 1:
            warnings.warn("dropout option adds dropout after all but last "
                          "recurrent layer, so non-zero dropout expects "
                          "num_layers greater than 1, but got dropout={} and "
                          "num_layers={}".format(dropout, num_layers))
        if proj_size < 0:
            raise ValueError("proj_size should be a positive integer or zero to disable projections")
        if proj_size >= hidden_size:
            raise ValueError("proj_size has to be smaller than hidden_size")

        if mode == 'LSTM':
            gate_size = 4 * hidden_size
        elif mode == 'GRU':
            gate_size = 3 * hidden_size
        elif mode == 'RNN_TANH':
            gate_size = hidden_size
        elif mode == 'RNN_RELU':
            gate_size = hidden_size
        else:
            raise ValueError("Unrecognized RNN mode: " + mode)

        self._flat_weights_names = []
        self._all_weights = []
        for layer in range(num_layers):
            for direction in range(num_directions):
                real_hidden_size = proj_size if proj_size > 0 else hidden_size
                layer_input_size = input_size if layer == 0 else real_hidden_size * num_directions

                w_ih = Parameter(torch.empty((gate_size, layer_input_size), **factory_kwargs))
                w_hh = Parameter(torch.empty((gate_size, real_hidden_size), **factory_kwargs))
                b_ih = Parameter(torch.empty(gate_size, **factory_kwargs))
                # Second bias vector included for CuDNN compatibility. Only one
                # bias vector is needed in standard definition.
                b_hh = Parameter(torch.empty(gate_size, **factory_kwargs))
                layer_params: Tuple[Tensor, ...] = ()
                if self.proj_size == 0:
                    if bias:
                        layer_params = (w_ih, w_hh, b_ih, b_hh)
                    else:
                        layer_params = (w_ih, w_hh)
                else:
                    w_hr = Parameter(torch.empty((proj_size, hidden_size), **factory_kwargs))
                    if bias:
                        layer_params = (w_ih, w_hh, b_ih, b_hh, w_hr)
                    else:
                        layer_params = (w_ih, w_hh, w_hr)

                suffix = '_reverse' if direction == 1 else ''
                param_names = ['weight_ih_l{}{}', 'weight_hh_l{}{}']
                if bias:
                    param_names += ['bias_ih_l{}{}', 'bias_hh_l{}{}']
                if self.proj_size > 0:
                    param_names += ['weight_hr_l{}{}']
                param_names = [x.format(layer, suffix) for x in param_names]

                for name, param in zip(param_names, layer_params):
                    setattr(self, name, param)
                self._flat_weights_names.extend(param_names)
                self._all_weights.append(param_names)

        self._flat_weights = [(lambda wn: getattr(self, wn) if hasattr(self, wn) else None)(wn) for wn in self._flat_weights_names]
        self.flatten_parameters()

        self.reset_parameters()

    def __setattr__(self, attr, value):
        if hasattr(self, "_flat_weights_names") and attr in self._flat_weights_names:
            # keep self._flat_weights up to date if you do self.weight = ...
            idx = self._flat_weights_names.index(attr)
            self._flat_weights[idx] = value
        super(RNNBase, self).__setattr__(attr, value)

    def flatten_parameters(self) -> None:
        """Resets parameter data pointer so that they can use faster code paths.

        Right now, this works only if the module is on the GPU and cuDNN is enabled.
        Otherwise, it's a no-op.
        """
        # Short-circuits if _flat_weights is only partially instantiated
        if len(self._flat_weights) != len(self._flat_weights_names):
            return

        for w in self._flat_weights:
            if not isinstance(w, Tensor):
                return
        # Short-circuits if any tensor in self._flat_weights is not acceptable to cuDNN
        # or the tensors in _flat_weights are of different dtypes

        first_fw = self._flat_weights[0]
        dtype = first_fw.dtype
        for fw in self._flat_weights:
            if (not isinstance(fw.data, Tensor) or not (fw.data.dtype == dtype) or
                    not fw.data.is_cuda or
                    not torch.backends.cudnn.is_acceptable(fw.data)):
                return

        # If any parameters alias, we fall back to the slower, copying code path. This is
        # a sufficient check, because overlapping parameter buffers that don't completely
        # alias would break the assumptions of the uniqueness check in
        # Module.named_parameters().
        unique_data_ptrs = set(p.data_ptr() for p in self._flat_weights)
        if len(unique_data_ptrs) != len(self._flat_weights):
            return

        with torch.cuda.device_of(first_fw):
            import torch.backends.cudnn.rnn as rnn

            # Note: no_grad() is necessary since _cudnn_rnn_flatten_weight is
            # an inplace operation on self._flat_weights
            with torch.no_grad():
                if torch._use_cudnn_rnn_flatten_weight():
                    num_weights = 4 if self.bias else 2
                    if self.proj_size > 0:
                        num_weights += 1
                    torch._cudnn_rnn_flatten_weight(
                        self._flat_weights, num_weights,
                        self.input_size, rnn.get_cudnn_mode(self.mode),
                        self.hidden_size, self.proj_size, self.num_layers,
                        self.batch_first, bool(self.bidirectional))

    def _apply(self, fn):
        ret = super(RNNBase, self)._apply(fn)

        # Resets _flat_weights
        # Note: be v. careful before removing this, as 3rd party device types
        # likely rely on this behavior to properly .to() modules like LSTM.
        self._flat_weights = [(lambda wn: getattr(self, wn) if hasattr(self, wn) else None)(wn) for wn in self._flat_weights_names]
        # Flattens params (on CUDA)
        self.flatten_parameters()

        return ret

    def reset_parameters(self) -> None:
        stdv = 1.0 / math.sqrt(self.hidden_size)
        for weight in self.parameters():
            init.uniform_(weight, -stdv, stdv)

    def check_input(self, input: Tensor, batch_sizes: Optional[Tensor]) -> None:
        expected_input_dim = 2 if batch_sizes is not None else 3
        if input.dim() != expected_input_dim:
            raise RuntimeError(
                'input must have {} dimensions, got {}'.format(
                    expected_input_dim, input.dim()))
        if self.input_size != input.size(-1):
            raise RuntimeError(
                'input.size(-1) must be equal to input_size. Expected {}, got {}'.format(
                    self.input_size, input.size(-1)))

    def get_expected_hidden_size(self, input: Tensor, batch_sizes: Optional[Tensor]) -> Tuple[int, int, int]:
        if batch_sizes is not None:
            mini_batch = int(batch_sizes[0])
        else:
            mini_batch = input.size(0) if self.batch_first else input.size(1)
        num_directions = 2 if self.bidirectional else 1
        if self.proj_size > 0:
            expected_hidden_size = (self.num_layers * num_directions,
                                    mini_batch, self.proj_size)
        else:
            expected_hidden_size = (self.num_layers * num_directions,
                                    mini_batch, self.hidden_size)
        return expected_hidden_size

    def check_hidden_size(self, hx: Tensor, expected_hidden_size: Tuple[int, int, int],
                          msg: str = 'Expected hidden size {}, got {}') -> None:
        if hx.size() != expected_hidden_size:
            raise RuntimeError(msg.format(expected_hidden_size, list(hx.size())))

    def check_forward_args(self, input: Tensor, hidden: Tensor, batch_sizes: Optional[Tensor]):
        self.check_input(input, batch_sizes)
        expected_hidden_size = self.get_expected_hidden_size(input, batch_sizes)

        self.check_hidden_size(hidden, expected_hidden_size)

    def permute_hidden(self, hx: Tensor, permutation: Optional[Tensor]):
        if permutation is None:
            return hx
        return apply_permutation(hx, permutation)

    def forward(self,
                input: Union[Tensor, PackedSequence],
                hx: Optional[Tensor] = None) -> Tuple[Union[Tensor, PackedSequence], Tensor]:
        is_packed = isinstance(input, PackedSequence)
        if is_packed:
            input, batch_sizes, sorted_indices, unsorted_indices = input
            max_batch_size = int(batch_sizes[0])
        else:
            input = cast(Tensor, input)
            batch_sizes = None
            max_batch_size = input.size(0) if self.batch_first else input.size(1)
            sorted_indices = None
            unsorted_indices = None
        if hx is None:
            input = cast(Tensor, input)
            num_directions = 2 if self.bidirectional else 1
            hx = torch.zeros(self.num_layers * num_directions,
                             max_batch_size, self.hidden_size,
                             dtype=input.dtype, device=input.device)
        else:
            # Each batch of the hidden state should match the input sequence that
            # the user believes he/she is passing in.
            hx = self.permute_hidden(hx, sorted_indices)

        assert hx is not None
        input = cast(Tensor, input)
        self.check_forward_args(input, hx, batch_sizes)
        _impl = _rnn_impls[self.mode]
        if batch_sizes is None:
            result = _impl(input, hx, self._flat_weights, self.bias, self.num_layers,
                           self.dropout, self.training, self.bidirectional, self.batch_first)
        else:
            result = _impl(input, batch_sizes, hx, self._flat_weights, self.bias,
                           self.num_layers, self.dropout, self.training, self.bidirectional)

        output: Union[Tensor, PackedSequence]
        output = result[0]
        hidden = result[1]

        if is_packed:
            output = PackedSequence(output, batch_sizes, sorted_indices, unsorted_indices)
        return output, self.permute_hidden(hidden, unsorted_indices)

    def extra_repr(self) -> str:
        s = '{input_size}, {hidden_size}'
        if self.proj_size != 0:
            s += ', proj_size={proj_size}'
        if self.num_layers != 1:
            s += ', num_layers={num_layers}'
        if self.bias is not True:
            s += ', bias={bias}'
        if self.batch_first is not False:
            s += ', batch_first={batch_first}'
        if self.dropout != 0:
            s += ', dropout={dropout}'
        if self.bidirectional is not False:
            s += ', bidirectional={bidirectional}'
        return s.format(**self.__dict__)

    def __setstate__(self, d):
        super(RNNBase, self).__setstate__(d)
        if 'all_weights' in d:
            self._all_weights = d['all_weights']
        # In PyTorch 1.8 we added a proj_size member variable to LSTM.
        # LSTMs that were serialized via torch.save(module) before PyTorch 1.8
        # don't have it, so to preserve compatibility we set proj_size here.
        if 'proj_size' not in d:
            self.proj_size = 0

        if isinstance(self._all_weights[0][0], str):
            return
        num_layers = self.num_layers
        num_directions = 2 if self.bidirectional else 1
        self._flat_weights_names = []
        self._all_weights = []
        for layer in range(num_layers):
            for direction in range(num_directions):
                suffix = '_reverse' if direction == 1 else ''
                weights = ['weight_ih_l{}{}', 'weight_hh_l{}{}', 'bias_ih_l{}{}',
                           'bias_hh_l{}{}', 'weight_hr_l{}{}']
                weights = [x.format(layer, suffix) for x in weights]
                if self.bias:
                    if self.proj_size > 0:
                        self._all_weights += [weights]
                        self._flat_weights_names.extend(weights)
                    else:
                        self._all_weights += [weights[:4]]
                        self._flat_weights_names.extend(weights[:4])
                else:
                    if self.proj_size > 0:
                        self._all_weights += [weights[:2]] + [weights[-1:]]
                        self._flat_weights_names.extend(weights[:2] + [weights[-1:]])
                    else:
                        self._all_weights += [weights[:2]]
                        self._flat_weights_names.extend(weights[:2])
        self._flat_weights = [(lambda wn: getattr(self, wn) if hasattr(self, wn) else None)(wn) for wn in self._flat_weights_names]

    @property
    def all_weights(self) -> List[List[Parameter]]:
        return [[getattr(self, weight) for weight in weights] for weights in self._all_weights]

    def _replicate_for_data_parallel(self):
        replica = super(RNNBase, self)._replicate_for_data_parallel()
        # Need to copy these caches, otherwise the replica will share the same
        # flat weights list.
        replica._flat_weights = replica._flat_weights[:]
        replica._flat_weights_names = replica._flat_weights_names[:]
        return replica


class RNN(RNNBase):
    r"""Applies a multi-layer Elman RNN with :math:`\tanh` or :math:`\text{ReLU}` non-linearity to an
    input sequence.


    For each element in the input sequence, each layer computes the following
    function:

    .. math::
        h_t = \tanh(W_{ih} x_t + b_{ih} + W_{hh} h_{(t-1)} + b_{hh})

    where :math:`h_t` is the hidden state at time `t`, :math:`x_t` is
    the input at time `t`, and :math:`h_{(t-1)}` is the hidden state of the
    previous layer at time `t-1` or the initial hidden state at time `0`.
    If :attr:`nonlinearity` is ``'relu'``, then :math:`\text{ReLU}` is used instead of :math:`\tanh`.

    Args:
        input_size: The number of expected features in the input `x`
        hidden_size: The number of features in the hidden state `h`
        num_layers: Number of recurrent layers. E.g., setting ``num_layers=2``
            would mean stacking two RNNs together to form a `stacked RNN`,
            with the second RNN taking in outputs of the first RNN and
            computing the final results. Default: 1
        nonlinearity: The non-linearity to use. Can be either ``'tanh'`` or ``'relu'``. Default: ``'tanh'``
        bias: If ``False``, then the layer does not use bias weights `b_ih` and `b_hh`.
            Default: ``True``
        batch_first: If ``True``, then the input and output tensors are provided
            as `(batch, seq, feature)` instead of `(seq, batch, feature)`.
            Note that this does not apply to hidden or cell states. See the
            Inputs/Outputs sections below for details.  Default: ``False``
        dropout: If non-zero, introduces a `Dropout` layer on the outputs of each
            RNN layer except the last layer, with dropout probability equal to
            :attr:`dropout`. Default: 0
        bidirectional: If ``True``, becomes a bidirectional RNN. Default: ``False``

    Inputs: input, h_0
        * **input**: tensor of shape :math:`(L, N, H_{in})` when ``batch_first=False`` or
          :math:`(N, L, H_{in})` when ``batch_first=True`` containing the features of
          the input sequence.  The input can also be a packed variable length sequence.
          See :func:`torch.nn.utils.rnn.pack_padded_sequence` or
          :func:`torch.nn.utils.rnn.pack_sequence` for details.
        * **h_0**: tensor of shape :math:`(D * \text{num\_layers}, N, H_{out})` containing the initial hidden
          state for each element in the batch. Defaults to zeros if not provided.

        where:

        .. math::
            \begin{aligned}
                N ={} & \text{batch size} \\
                L ={} & \text{sequence length} \\
                D ={} & 2 \text{ if bidirectional=True otherwise } 1 \\
                H_{in} ={} & \text{input\_size} \\
                H_{out} ={} & \text{hidden\_size}
            \end{aligned}

    Outputs: output, h_n
        * **output**: tensor of shape :math:`(L, N, D * H_{out})` when ``batch_first=False`` or
          :math:`(N, L, D * H_{out})` when ``batch_first=True`` containing the output features
          `(h_t)` from the last layer of the RNN, for each `t`. If a
          :class:`torch.nn.utils.rnn.PackedSequence` has been given as the input, the output
          will also be a packed sequence.
        * **h_n**: tensor of shape :math:`(D * \text{num\_layers}, N, H_{out})` containing the final hidden state
          for each element in the batch.

    Attributes:
        weight_ih_l[k]: the learnable input-hidden weights of the k-th layer,
            of shape `(hidden_size, input_size)` for `k = 0`. Otherwise, the shape is
            `(hidden_size, num_directions * hidden_size)`
        weight_hh_l[k]: the learnable hidden-hidden weights of the k-th layer,
            of shape `(hidden_size, hidden_size)`
        bias_ih_l[k]: the learnable input-hidden bias of the k-th layer,
            of shape `(hidden_size)`
        bias_hh_l[k]: the learnable hidden-hidden bias of the k-th layer,
            of shape `(hidden_size)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    .. note::
        For bidirectional RNNs, forward and backward are directions 0 and 1 respectively.
        Example of splitting the output layers when ``batch_first=False``:
        ``output.view(seq_len, batch, num_directions, hidden_size)``.

    .. include:: ../cudnn_rnn_determinism.rst

    .. include:: ../cudnn_persistent_rnn.rst

    Examples::

        >>> rnn = nn.RNN(10, 20, 2)
        >>> input = torch.randn(5, 3, 10)
        >>> h0 = torch.randn(2, 3, 20)
        >>> output, hn = rnn(input, h0)
    """

    def __init__(self, *args, **kwargs):
        if 'proj_size' in kwargs:
            raise ValueError("proj_size argument is only supported for LSTM, not RNN or GRU")
        self.nonlinearity = kwargs.pop('nonlinearity', 'tanh')
        if self.nonlinearity == 'tanh':
            mode = 'RNN_TANH'
        elif self.nonlinearity == 'relu':
            mode = 'RNN_RELU'
        else:
            raise ValueError("Unknown nonlinearity '{}'".format(self.nonlinearity))
        super(RNN, self).__init__(mode, *args, **kwargs)


# XXX: LSTM and GRU implementation is different from RNNBase, this is because:
# 1. we want to support nn.LSTM and nn.GRU in TorchScript and TorchScript in
#    its current state could not support the python Union Type or Any Type
# 2. TorchScript static typing does not allow a Function or Callable type in
#    Dict values, so we have to separately call _VF instead of using _rnn_impls
# 3. This is temporary only and in the transition state that we want to make it
#    on time for the release
#
# More discussion details in https://github.com/pytorch/pytorch/pull/23266
#
# TODO: remove the overriding implementations for LSTM and GRU when TorchScript
# support expressing these two modules generally.
class LSTM(RNNBase):
    r"""Applies a multi-layer long short-term memory (LSTM) RNN to an input
    sequence.


    For each element in the input sequence, each layer computes the following
    function:

    .. math::
        \begin{array}{ll} \\
            i_t = \sigma(W_{ii} x_t + b_{ii} + W_{hi} h_{t-1} + b_{hi}) \\
            f_t = \sigma(W_{if} x_t + b_{if} + W_{hf} h_{t-1} + b_{hf}) \\
            g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hg} h_{t-1} + b_{hg}) \\
            o_t = \sigma(W_{io} x_t + b_{io} + W_{ho} h_{t-1} + b_{ho}) \\
            c_t = f_t \odot c_{t-1} + i_t \odot g_t \\
            h_t = o_t \odot \tanh(c_t) \\
        \end{array}

    where :math:`h_t` is the hidden state at time `t`, :math:`c_t` is the cell
    state at time `t`, :math:`x_t` is the input at time `t`, :math:`h_{t-1}`
    is the hidden state of the layer at time `t-1` or the initial hidden
    state at time `0`, and :math:`i_t`, :math:`f_t`, :math:`g_t`,
    :math:`o_t` are the input, forget, cell, and output gates, respectively.
    :math:`\sigma` is the sigmoid function, and :math:`\odot` is the Hadamard product.

    In a multilayer LSTM, the input :math:`x^{(l)}_t` of the :math:`l` -th layer
    (:math:`l >= 2`) is the hidden state :math:`h^{(l-1)}_t` of the previous layer multiplied by
    dropout :math:`\delta^{(l-1)}_t` where each :math:`\delta^{(l-1)}_t` is a Bernoulli random
    variable which is :math:`0` with probability :attr:`dropout`.

    If ``proj_size > 0`` is specified, LSTM with projections will be used. This changes
    the LSTM cell in the following way. First, the dimension of :math:`h_t` will be changed from
    ``hidden_size`` to ``proj_size`` (dimensions of :math:`W_{hi}` will be changed accordingly).
    Second, the output hidden state of each layer will be multiplied by a learnable projection
    matrix: :math:`h_t = W_{hr}h_t`. Note that as a consequence of this, the output
    of LSTM network will be of different shape as well. See Inputs/Outputs sections below for exact
    dimensions of all variables. You can find more details in https://arxiv.org/abs/1402.1128.

    Args:
        input_size: The number of expected features in the input `x`
        hidden_size: The number of features in the hidden state `h`
        num_layers: Number of recurrent layers. E.g., setting ``num_layers=2``
            would mean stacking two LSTMs together to form a `stacked LSTM`,
            with the second LSTM taking in outputs of the first LSTM and
            computing the final results. Default: 1
        bias: If ``False``, then the layer does not use bias weights `b_ih` and `b_hh`.
            Default: ``True``
        batch_first: If ``True``, then the input and output tensors are provided
            as `(batch, seq, feature)` instead of `(seq, batch, feature)`.
            Note that this does not apply to hidden or cell states. See the
            Inputs/Outputs sections below for details.  Default: ``False``
        dropout: If non-zero, introduces a `Dropout` layer on the outputs of each
            LSTM layer except the last layer, with dropout probability equal to
            :attr:`dropout`. Default: 0
        bidirectional: If ``True``, becomes a bidirectional LSTM. Default: ``False``
        proj_size: If ``> 0``, will use LSTM with projections of corresponding size. Default: 0

    Inputs: input, (h_0, c_0)
        * **input**: tensor of shape :math:`(L, N, H_{in})` when ``batch_first=False`` or
          :math:`(N, L, H_{in})` when ``batch_first=True`` containing the features of
          the input sequence.  The input can also be a packed variable length sequence.
          See :func:`torch.nn.utils.rnn.pack_padded_sequence` or
          :func:`torch.nn.utils.rnn.pack_sequence` for details.
        * **h_0**: tensor of shape :math:`(D * \text{num\_layers}, N, H_{out})` containing the
          initial hidden state for each element in the batch.
          Defaults to zeros if (h_0, c_0) is not provided.
        * **c_0**: tensor of shape :math:`(D * \text{num\_layers}, N, H_{cell})` containing the
          initial cell state for each element in the batch.
          Defaults to zeros if (h_0, c_0) is not provided.

        where:

        .. math::
            \begin{aligned}
                N ={} & \text{batch size} \\
                L ={} & \text{sequence length} \\
                D ={} & 2 \text{ if bidirectional=True otherwise } 1 \\
                H_{in} ={} & \text{input\_size} \\
                H_{cell} ={} & \text{hidden\_size} \\
                H_{out} ={} & \text{proj\_size if } \text{proj\_size}>0 \text{ otherwise hidden\_size} \\
            \end{aligned}

    Outputs: output, (h_n, c_n)
        * **output**: tensor of shape :math:`(L, N, D * H_{out})` when ``batch_first=False`` or
          :math:`(N, L, D * H_{out})` when ``batch_first=True`` containing the output features
          `(h_t)` from the last layer of the LSTM, for each `t`. If a
          :class:`torch.nn.utils.rnn.PackedSequence` has been given as the input, the output
          will also be a packed sequence.
        * **h_n**: tensor of shape :math:`(D * \text{num\_layers}, N, H_{out})` containing the
          final hidden state for each element in the batch.
        * **c_n**: tensor of shape :math:`(D * \text{num\_layers}, N, H_{cell})` containing the
          final cell state for each element in the batch.

    Attributes:
        weight_ih_l[k] : the learnable input-hidden weights of the :math:`\text{k}^{th}` layer
            `(W_ii|W_if|W_ig|W_io)`, of shape `(4*hidden_size, input_size)` for `k = 0`.
            Otherwise, the shape is `(4*hidden_size, num_directions * hidden_size)`. If
            ``proj_size > 0`` was specified, the shape will be
            `(4*hidden_size, num_directions * proj_size)` for `k > 0`
        weight_hh_l[k] : the learnable hidden-hidden weights of the :math:`\text{k}^{th}` layer
            `(W_hi|W_hf|W_hg|W_ho)`, of shape `(4*hidden_size, hidden_size)`. If ``proj_size > 0``
            was specified, the shape will be `(4*hidden_size, proj_size)`.
        bias_ih_l[k] : the learnable input-hidden bias of the :math:`\text{k}^{th}` layer
            `(b_ii|b_if|b_ig|b_io)`, of shape `(4*hidden_size)`
        bias_hh_l[k] : the learnable hidden-hidden bias of the :math:`\text{k}^{th}` layer
            `(b_hi|b_hf|b_hg|b_ho)`, of shape `(4*hidden_size)`
        weight_hr_l[k] : the learnable projection weights of the :math:`\text{k}^{th}` layer
            of shape `(proj_size, hidden_size)`. Only present when ``proj_size > 0`` was
            specified.
        weight_ih_l[k]_reverse: Analogous to `weight_ih_l[k]` for the reverse direction.
            Only present when ``bidirectional=True``.
        weight_hh_l[k]_reverse:  Analogous to `weight_hh_l[k]` for the reverse direction.
            Only present when ``bidirectional=True``.
        bias_ih_l[k]_reverse:  Analogous to `bias_ih_l[k]` for the reverse direction.
            Only present when ``bidirectional=True``.
        bias_hh_l[k]_reverse:  Analogous to `bias_hh_l[k]` for the reverse direction.
            Only present when ``bidirectional=True``.
        weight_hr_l[k]_reverse:  Analogous to `weight_hr_l[k]` for the reverse direction.
            Only present when ``bidirectional=True`` and ``proj_size > 0`` was specified.

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    .. note::
        For bidirectional LSTMs, forward and backward are directions 0 and 1 respectively.
        Example of splitting the output layers when ``batch_first=False``:
        ``output.view(seq_len, batch, num_directions, hidden_size)``.

    .. include:: ../cudnn_rnn_determinism.rst

    .. include:: ../cudnn_persistent_rnn.rst

    Examples::

        >>> rnn = nn.LSTM(10, 20, 2)
        >>> input = torch.randn(5, 3, 10)
        >>> h0 = torch.randn(2, 3, 20)
        >>> c0 = torch.randn(2, 3, 20)
        >>> output, (hn, cn) = rnn(input, (h0, c0))
    """

    def __init__(self, *args, **kwargs):
        super(LSTM, self).__init__('LSTM', *args, **kwargs)

    def get_expected_cell_size(self, input: Tensor, batch_sizes: Optional[Tensor]) -> Tuple[int, int, int]:
        if batch_sizes is not None:
            mini_batch = int(batch_sizes[0])
        else:
            mini_batch = input.size(0) if self.batch_first else input.size(1)
        num_directions = 2 if self.bidirectional else 1
        expected_hidden_size = (self.num_layers * num_directions,
                                mini_batch, self.hidden_size)
        return expected_hidden_size

    # In the future, we should prevent mypy from applying contravariance rules here.
    # See torch/nn/modules/module.py::_forward_unimplemented
    def check_forward_args(self,  # type: ignore[override]
                           input: Tensor,
                           hidden: Tuple[Tensor, Tensor],
                           batch_sizes: Optional[Tensor],
                           ):
        self.check_input(input, batch_sizes)
        self.check_hidden_size(hidden[0], self.get_expected_hidden_size(input, batch_sizes),
                               'Expected hidden[0] size {}, got {}')
        self.check_hidden_size(hidden[1], self.get_expected_cell_size(input, batch_sizes),
                               'Expected hidden[1] size {}, got {}')

    # Same as above, see torch/nn/modules/module.py::_forward_unimplemented
    def permute_hidden(self,  # type: ignore[override]
                       hx: Tuple[Tensor, Tensor],
                       permutation: Optional[Tensor]
                       ) -> Tuple[Tensor, Tensor]:
        if permutation is None:
            return hx
        return apply_permutation(hx[0], permutation), apply_permutation(hx[1], permutation)

    # Same as above, see torch/nn/modules/module.py::_forward_unimplemented
    @overload  # type: ignore[override]
    @torch._jit_internal._overload_method  # noqa: F811
    def forward(self, input: Tensor, hx: Optional[Tuple[Tensor, Tensor]] = None
                ) -> Tuple[Tensor, Tuple[Tensor, Tensor]]:  # noqa: F811
        pass

    # Same as above, see torch/nn/modules/module.py::_forward_unimplemented
    @overload
    @torch._jit_internal._overload_method  # noqa: F811
    def forward(self, input: PackedSequence, hx: Optional[Tuple[Tensor, Tensor]] = None
                ) -> Tuple[PackedSequence, Tuple[Tensor, Tensor]]:  # noqa: F811
        pass

    def forward(self, input, hx=None):  # noqa: F811
        orig_input = input
        # xxx: isinstance check needs to be in conditional for TorchScript to compile
        if isinstance(orig_input, PackedSequence):
            input, batch_sizes, sorted_indices, unsorted_indices = input
            max_batch_size = batch_sizes[0]
            max_batch_size = int(max_batch_size)
        else:
            batch_sizes = None
            max_batch_size = input.size(0) if self.batch_first else input.size(1)
            sorted_indices = None
            unsorted_indices = None

        if hx is None:
            num_directions = 2 if self.bidirectional else 1
            real_hidden_size = self.proj_size if self.proj_size > 0 else self.hidden_size
            h_zeros = torch.zeros(self.num_layers * num_directions,
                                  max_batch_size, real_hidden_size,
                                  dtype=input.dtype, device=input.device)
            c_zeros = torch.zeros(self.num_layers * num_directions,
                                  max_batch_size, self.hidden_size,
                                  dtype=input.dtype, device=input.device)
            hx = (h_zeros, c_zeros)
        else:
            # Each batch of the hidden state should match the input sequence that
            # the user believes he/she is passing in.
            hx = self.permute_hidden(hx, sorted_indices)

        self.check_forward_args(input, hx, batch_sizes)
        if batch_sizes is None:
            result = _VF.lstm(input, hx, self._flat_weights, self.bias, self.num_layers,
                              self.dropout, self.training, self.bidirectional, self.batch_first)
        else:
            result = _VF.lstm(input, batch_sizes, hx, self._flat_weights, self.bias,
                              self.num_layers, self.dropout, self.training, self.bidirectional)
        output = result[0]
        hidden = result[1:]
        # xxx: isinstance check needs to be in conditional for TorchScript to compile
        if isinstance(orig_input, PackedSequence):
            output_packed = PackedSequence(output, batch_sizes, sorted_indices, unsorted_indices)
            return output_packed, self.permute_hidden(hidden, unsorted_indices)
        else:
            return output, self.permute_hidden(hidden, unsorted_indices)


class GRU(RNNBase):
    r"""Applies a multi-layer gated recurrent unit (GRU) RNN to an input sequence.


    For each element in the input sequence, each layer computes the following
    function:

    .. math::
        \begin{array}{ll}
            r_t = \sigma(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
            z_t = \sigma(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
            n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\
            h_t = (1 - z_t) * n_t + z_t * h_{(t-1)}
        \end{array}

    where :math:`h_t` is the hidden state at time `t`, :math:`x_t` is the input
    at time `t`, :math:`h_{(t-1)}` is the hidden state of the layer
    at time `t-1` or the initial hidden state at time `0`, and :math:`r_t`,
    :math:`z_t`, :math:`n_t` are the reset, update, and new gates, respectively.
    :math:`\sigma` is the sigmoid function, and :math:`*` is the Hadamard product.

    In a multilayer GRU, the input :math:`x^{(l)}_t` of the :math:`l` -th layer
    (:math:`l >= 2`) is the hidden state :math:`h^{(l-1)}_t` of the previous layer multiplied by
    dropout :math:`\delta^{(l-1)}_t` where each :math:`\delta^{(l-1)}_t` is a Bernoulli random
    variable which is :math:`0` with probability :attr:`dropout`.

    Args:
        input_size: The number of expected features in the input `x`
        hidden_size: The number of features in the hidden state `h`
        num_layers: Number of recurrent layers. E.g., setting ``num_layers=2``
            would mean stacking two GRUs together to form a `stacked GRU`,
            with the second GRU taking in outputs of the first GRU and
            computing the final results. Default: 1
        bias: If ``False``, then the layer does not use bias weights `b_ih` and `b_hh`.
            Default: ``True``
        batch_first: If ``True``, then the input and output tensors are provided
            as `(batch, seq, feature)` instead of `(seq, batch, feature)`.
            Note that this does not apply to hidden or cell states. See the
            Inputs/Outputs sections below for details.  Default: ``False``
        dropout: If non-zero, introduces a `Dropout` layer on the outputs of each
            GRU layer except the last layer, with dropout probability equal to
            :attr:`dropout`. Default: 0
        bidirectional: If ``True``, becomes a bidirectional GRU. Default: ``False``

    Inputs: input, h_0
        * **input**: tensor of shape :math:`(L, N, H_{in})` when ``batch_first=False`` or
          :math:`(N, L, H_{in})` when ``batch_first=True`` containing the features of
          the input sequence.  The input can also be a packed variable length sequence.
          See :func:`torch.nn.utils.rnn.pack_padded_sequence` or
          :func:`torch.nn.utils.rnn.pack_sequence` for details.
        * **h_0**: tensor of shape :math:`(D * \text{num\_layers}, N, H_{out})` containing the initial hidden
          state for each element in the batch. Defaults to zeros if not provided.

        where:

        .. math::
            \begin{aligned}
                N ={} & \text{batch size} \\
                L ={} & \text{sequence length} \\
                D ={} & 2 \text{ if bidirectional=True otherwise } 1 \\
                H_{in} ={} & \text{input\_size} \\
                H_{out} ={} & \text{hidden\_size}
            \end{aligned}

    Outputs: output, h_n
        * **output**: tensor of shape :math:`(L, N, D * H_{out})` when ``batch_first=False`` or
          :math:`(N, L, D * H_{out})` when ``batch_first=True`` containing the output features
          `(h_t)` from the last layer of the GRU, for each `t`. If a
          :class:`torch.nn.utils.rnn.PackedSequence` has been given as the input, the output
          will also be a packed sequence.
        * **h_n**: tensor of shape :math:`(D * \text{num\_layers}, N, H_{out})` containing the final hidden state
          for each element in the batch.

    Attributes:
        weight_ih_l[k] : the learnable input-hidden weights of the :math:`\text{k}^{th}` layer
            (W_ir|W_iz|W_in), of shape `(3*hidden_size, input_size)` for `k = 0`.
            Otherwise, the shape is `(3*hidden_size, num_directions * hidden_size)`
        weight_hh_l[k] : the learnable hidden-hidden weights of the :math:`\text{k}^{th}` layer
            (W_hr|W_hz|W_hn), of shape `(3*hidden_size, hidden_size)`
        bias_ih_l[k] : the learnable input-hidden bias of the :math:`\text{k}^{th}` layer
            (b_ir|b_iz|b_in), of shape `(3*hidden_size)`
        bias_hh_l[k] : the learnable hidden-hidden bias of the :math:`\text{k}^{th}` layer
            (b_hr|b_hz|b_hn), of shape `(3*hidden_size)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    .. note::
        For bidirectional GRUs, forward and backward are directions 0 and 1 respectively.
        Example of splitting the output layers when ``batch_first=False``:
        ``output.view(seq_len, batch, num_directions, hidden_size)``.

    .. include:: ../cudnn_persistent_rnn.rst

    Examples::

        >>> rnn = nn.GRU(10, 20, 2)
        >>> input = torch.randn(5, 3, 10)
        >>> h0 = torch.randn(2, 3, 20)
        >>> output, hn = rnn(input, h0)
    """

    def __init__(self, *args, **kwargs):
        if 'proj_size' in kwargs:
            raise ValueError("proj_size argument is only supported for LSTM, not RNN or GRU")
        super(GRU, self).__init__('GRU', *args, **kwargs)

    @overload  # type: ignore[override]
    @torch._jit_internal._overload_method  # noqa: F811
    def forward(self, input: Tensor, hx: Optional[Tensor] = None) -> Tuple[Tensor, Tensor]:  # noqa: F811
        pass

    @overload
    @torch._jit_internal._overload_method  # noqa: F811
    def forward(self, input: PackedSequence, hx: Optional[Tensor] = None) -> Tuple[PackedSequence, Tensor]:  # noqa: F811
        pass

    def forward(self, input, hx=None):  # noqa: F811
        orig_input = input
        # xxx: isinstance check needs to be in conditional for TorchScript to compile
        if isinstance(orig_input, PackedSequence):
            input, batch_sizes, sorted_indices, unsorted_indices = input
            max_batch_size = batch_sizes[0]
            max_batch_size = int(max_batch_size)
        else:
            batch_sizes = None
            max_batch_size = input.size(0) if self.batch_first else input.size(1)
            sorted_indices = None
            unsorted_indices = None

        if hx is None:
            num_directions = 2 if self.bidirectional else 1
            hx = torch.zeros(self.num_layers * num_directions,
                             max_batch_size, self.hidden_size,
                             dtype=input.dtype, device=input.device)
        else:
            # Each batch of the hidden state should match the input sequence that
            # the user believes he/she is passing in.
            hx = self.permute_hidden(hx, sorted_indices)

        self.check_forward_args(input, hx, batch_sizes)
        if batch_sizes is None:
            result = _VF.gru(input, hx, self._flat_weights, self.bias, self.num_layers,
                             self.dropout, self.training, self.bidirectional, self.batch_first)
        else:
            result = _VF.gru(input, batch_sizes, hx, self._flat_weights, self.bias,
                             self.num_layers, self.dropout, self.training, self.bidirectional)
        output = result[0]
        hidden = result[1]

        # xxx: isinstance check needs to be in conditional for TorchScript to compile
        if isinstance(orig_input, PackedSequence):
            output_packed = PackedSequence(output, batch_sizes, sorted_indices, unsorted_indices)
            return output_packed, self.permute_hidden(hidden, unsorted_indices)
        else:
            return output, self.permute_hidden(hidden, unsorted_indices)


class RNNCellBase(Module):
    __constants__ = ['input_size', 'hidden_size', 'bias']

    input_size: int
    hidden_size: int
    bias: bool
    weight_ih: Tensor
    weight_hh: Tensor
    # WARNING: bias_ih and bias_hh purposely not defined here.
    # See https://github.com/pytorch/pytorch/issues/39670

    def __init__(self, input_size: int, hidden_size: int, bias: bool, num_chunks: int,
                 device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(RNNCellBase, self).__init__()
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.bias = bias
        self.weight_ih = Parameter(torch.empty((num_chunks * hidden_size, input_size), **factory_kwargs))
        self.weight_hh = Parameter(torch.empty((num_chunks * hidden_size, hidden_size), **factory_kwargs))
        if bias:
            self.bias_ih = Parameter(torch.empty(num_chunks * hidden_size, **factory_kwargs))
            self.bias_hh = Parameter(torch.empty(num_chunks * hidden_size, **factory_kwargs))
        else:
            self.register_parameter('bias_ih', None)
            self.register_parameter('bias_hh', None)

        self.reset_parameters()

    def extra_repr(self) -> str:
        s = '{input_size}, {hidden_size}'
        if 'bias' in self.__dict__ and self.bias is not True:
            s += ', bias={bias}'
        if 'nonlinearity' in self.__dict__ and self.nonlinearity != "tanh":
            s += ', nonlinearity={nonlinearity}'
        return s.format(**self.__dict__)

    def reset_parameters(self) -> None:
        stdv = 1.0 / math.sqrt(self.hidden_size)
        for weight in self.parameters():
            init.uniform_(weight, -stdv, stdv)


class RNNCell(RNNCellBase):
    r"""An Elman RNN cell with tanh or ReLU non-linearity.

    .. math::

        h' = \tanh(W_{ih} x + b_{ih}  +  W_{hh} h + b_{hh})

    If :attr:`nonlinearity` is `'relu'`, then ReLU is used in place of tanh.

    Args:
        input_size: The number of expected features in the input `x`
        hidden_size: The number of features in the hidden state `h`
        bias: If ``False``, then the layer does not use bias weights `b_ih` and `b_hh`.
            Default: ``True``
        nonlinearity: The non-linearity to use. Can be either ``'tanh'`` or ``'relu'``. Default: ``'tanh'``

    Inputs: input, hidden
        - **input** of shape `(batch, input_size)`: tensor containing input features
        - **hidden** of shape `(batch, hidden_size)`: tensor containing the initial hidden
          state for each element in the batch.
          Defaults to zero if not provided.

    Outputs: h'
        - **h'** of shape `(batch, hidden_size)`: tensor containing the next hidden state
          for each element in the batch

    Shape:
        - Input1: :math:`(N, H_{in})` tensor containing input features where
          :math:`H_{in}` = `input_size`
        - Input2: :math:`(N, H_{out})` tensor containing the initial hidden
          state for each element in the batch where :math:`H_{out}` = `hidden_size`
          Defaults to zero if not provided.
        - Output: :math:`(N, H_{out})` tensor containing the next hidden state
          for each element in the batch

    Attributes:
        weight_ih: the learnable input-hidden weights, of shape
            `(hidden_size, input_size)`
        weight_hh: the learnable hidden-hidden weights, of shape
            `(hidden_size, hidden_size)`
        bias_ih: the learnable input-hidden bias, of shape `(hidden_size)`
        bias_hh: the learnable hidden-hidden bias, of shape `(hidden_size)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    Examples::

        >>> rnn = nn.RNNCell(10, 20)
        >>> input = torch.randn(6, 3, 10)
        >>> hx = torch.randn(3, 20)
        >>> output = []
        >>> for i in range(6):
                hx = rnn(input[i], hx)
                output.append(hx)
    """
    __constants__ = ['input_size', 'hidden_size', 'bias', 'nonlinearity']
    nonlinearity: str

    def __init__(self, input_size: int, hidden_size: int, bias: bool = True, nonlinearity: str = "tanh",
                 device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(RNNCell, self).__init__(input_size, hidden_size, bias, num_chunks=1, **factory_kwargs)
        self.nonlinearity = nonlinearity

    def forward(self, input: Tensor, hx: Optional[Tensor] = None) -> Tensor:
        if hx is None:
            hx = torch.zeros(input.size(0), self.hidden_size, dtype=input.dtype, device=input.device)
        if self.nonlinearity == "tanh":
            ret = _VF.rnn_tanh_cell(
                input, hx,
                self.weight_ih, self.weight_hh,
                self.bias_ih, self.bias_hh,
            )
        elif self.nonlinearity == "relu":
            ret = _VF.rnn_relu_cell(
                input, hx,
                self.weight_ih, self.weight_hh,
                self.bias_ih, self.bias_hh,
            )
        else:
            ret = input  # TODO: remove when jit supports exception flow
            raise RuntimeError(
                "Unknown nonlinearity: {}".format(self.nonlinearity))
        return ret


class LSTMCell(RNNCellBase):
    r"""A long short-term memory (LSTM) cell.

    .. math::

        \begin{array}{ll}
        i = \sigma(W_{ii} x + b_{ii} + W_{hi} h + b_{hi}) \\
        f = \sigma(W_{if} x + b_{if} + W_{hf} h + b_{hf}) \\
        g = \tanh(W_{ig} x + b_{ig} + W_{hg} h + b_{hg}) \\
        o = \sigma(W_{io} x + b_{io} + W_{ho} h + b_{ho}) \\
        c' = f * c + i * g \\
        h' = o * \tanh(c') \\
        \end{array}

    where :math:`\sigma` is the sigmoid function, and :math:`*` is the Hadamard product.

    Args:
        input_size: The number of expected features in the input `x`
        hidden_size: The number of features in the hidden state `h`
        bias: If ``False``, then the layer does not use bias weights `b_ih` and
            `b_hh`. Default: ``True``

    Inputs: input, (h_0, c_0)
        - **input** of shape `(batch, input_size)`: tensor containing input features
        - **h_0** of shape `(batch, hidden_size)`: tensor containing the initial hidden
          state for each element in the batch.
        - **c_0** of shape `(batch, hidden_size)`: tensor containing the initial cell state
          for each element in the batch.

          If `(h_0, c_0)` is not provided, both **h_0** and **c_0** default to zero.

    Outputs: (h_1, c_1)
        - **h_1** of shape `(batch, hidden_size)`: tensor containing the next hidden state
          for each element in the batch
        - **c_1** of shape `(batch, hidden_size)`: tensor containing the next cell state
          for each element in the batch

    Attributes:
        weight_ih: the learnable input-hidden weights, of shape
            `(4*hidden_size, input_size)`
        weight_hh: the learnable hidden-hidden weights, of shape
            `(4*hidden_size, hidden_size)`
        bias_ih: the learnable input-hidden bias, of shape `(4*hidden_size)`
        bias_hh: the learnable hidden-hidden bias, of shape `(4*hidden_size)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    Examples::

        >>> rnn = nn.LSTMCell(10, 20) # (input_size, hidden_size)
        >>> input = torch.randn(2, 3, 10) # (time_steps, batch, input_size)
        >>> hx = torch.randn(3, 20) # (batch, hidden_size)
        >>> cx = torch.randn(3, 20)
        >>> output = []
        >>> for i in range(input.size()[0]):
                hx, cx = rnn(input[i], (hx, cx))
                output.append(hx)
        >>> output = torch.stack(output, dim=0)
    """

    def __init__(self, input_size: int, hidden_size: int, bias: bool = True,
                 device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(LSTMCell, self).__init__(input_size, hidden_size, bias, num_chunks=4, **factory_kwargs)

    def forward(self, input: Tensor, hx: Optional[Tuple[Tensor, Tensor]] = None) -> Tuple[Tensor, Tensor]:
        if hx is None:
            zeros = torch.zeros(input.size(0), self.hidden_size, dtype=input.dtype, device=input.device)
            hx = (zeros, zeros)
        return _VF.lstm_cell(
            input, hx,
            self.weight_ih, self.weight_hh,
            self.bias_ih, self.bias_hh,
        )


class GRUCell(RNNCellBase):
    r"""A gated recurrent unit (GRU) cell

    .. math::

        \begin{array}{ll}
        r = \sigma(W_{ir} x + b_{ir} + W_{hr} h + b_{hr}) \\
        z = \sigma(W_{iz} x + b_{iz} + W_{hz} h + b_{hz}) \\
        n = \tanh(W_{in} x + b_{in} + r * (W_{hn} h + b_{hn})) \\
        h' = (1 - z) * n + z * h
        \end{array}

    where :math:`\sigma` is the sigmoid function, and :math:`*` is the Hadamard product.

    Args:
        input_size: The number of expected features in the input `x`
        hidden_size: The number of features in the hidden state `h`
        bias: If ``False``, then the layer does not use bias weights `b_ih` and
            `b_hh`. Default: ``True``

    Inputs: input, hidden
        - **input** of shape `(batch, input_size)`: tensor containing input features
        - **hidden** of shape `(batch, hidden_size)`: tensor containing the initial hidden
          state for each element in the batch.
          Defaults to zero if not provided.

    Outputs: h'
        - **h'** of shape `(batch, hidden_size)`: tensor containing the next hidden state
          for each element in the batch

    Shape:
        - Input1: :math:`(N, H_{in})` tensor containing input features where
          :math:`H_{in}` = `input_size`
        - Input2: :math:`(N, H_{out})` tensor containing the initial hidden
          state for each element in the batch where :math:`H_{out}` = `hidden_size`
          Defaults to zero if not provided.
        - Output: :math:`(N, H_{out})` tensor containing the next hidden state
          for each element in the batch

    Attributes:
        weight_ih: the learnable input-hidden weights, of shape
            `(3*hidden_size, input_size)`
        weight_hh: the learnable hidden-hidden weights, of shape
            `(3*hidden_size, hidden_size)`
        bias_ih: the learnable input-hidden bias, of shape `(3*hidden_size)`
        bias_hh: the learnable hidden-hidden bias, of shape `(3*hidden_size)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    Examples::

        >>> rnn = nn.GRUCell(10, 20)
        >>> input = torch.randn(6, 3, 10)
        >>> hx = torch.randn(3, 20)
        >>> output = []
        >>> for i in range(6):
                hx = rnn(input[i], hx)
                output.append(hx)
    """

    def __init__(self, input_size: int, hidden_size: int, bias: bool = True,
                 device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(GRUCell, self).__init__(input_size, hidden_size, bias, num_chunks=3, **factory_kwargs)

    def forward(self, input: Tensor, hx: Optional[Tensor] = None) -> Tensor:
        if hx is None:
            hx = torch.zeros(input.size(0), self.hidden_size, dtype=input.dtype, device=input.device)
        return _VF.gru_cell(
            input, hx,
            self.weight_ih, self.weight_hh,
            self.bias_ih, self.bias_hh,
        )
